Constant-Depth circuits for arithmetic in finite fields of characteristic two

Authors:
Alexander Healy;Emanuele Viola
Affiliations:
Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA;Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA
Venue:
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Year:
2006

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Abstract

We study the complexity of arithmetic in finite fields of characteristic two, $\mathbb{F}_{2^n}$. We concentrate on the following two problems: – Iterated Multiplication: Given $\alpha_1,...,\alpha_t \in \mathbb{F}_{2^n}$, compute α1 ⋯ αt. – Exponentiation: Given $\alpha \in \mathbb{F}_{2^n}$ and a t-bit integer k, compute αk.